I can't really advise.
The car environment is electronically dirty.
You need to make sure that connections between anything don't come loose due to vibrations. This basically will exclude all boards with headers like Uno. A dedicated PCB is your best option; if needed something like a SparkFun Pro Mini, Arduino Nano or similar in a socket on that PCB.
You need a driver for the actuator; maybe a relay, maybe a H-bridge. You will need to know the specs of the actuator (current consumption, voltage) to decide on the suitable driver.
The servo control signal can be connected directly to the processor (together with ground).
And that's about how far I can help.